This is truly the last resort! As I don't suggest you walking around the whole town, unless you can walk a 10K+, in Florida's nice, hot, sizzlin' summers, I would suggest a taxi, only to get from point A to point B. As we all know, taxis can become expensive. I have some listed below, just in case you come to your last resort. Some even have flat rates to certain locations, which is good to know for reference. If you stay at a hotel and you are nice enough to the front desk attendants, they might be so kind to call one for you. :)
Brevard Yellow Cab
Cab To Go
A Phoenix Cab Service
I mentioned to you the limitations of our airport. Now, let me tell you the good part! Most of the car rental agencies are located in the airport!
Here are the agencies:
You have to know that even though Melbourne is a decent size city, we aren't catching up with Orlando that fast. We do have an airport located in the city, however it is extremely limited! I would have to say that most local businessmen and women use it. There are some good flights that Delta offers around the country. My honest and only suggestion is to fly into Orlando, because that will be the closest airport. An interesting fact is that we have a lot of FIT students who fly from this airport to log hours. The airport does offer other great services in transportation.
While there is Spacecoast transit, I think this is one place you'll want a car. They are easy to get at low prices in Orlando